More rambling speculation...

The earth's "natural" frequency has been stated to be ~7.8 Hertz
(cycles per second) also known as the Schumann Resonance (actually
7.83 Hz ). All prior attempts to tap into it have failed. One
wonders if 2.5 Hz is also natural to some (presumably larger)
system like our sun or a nearby neutron star or black hole) - and
if there is a coupling mechanism to smaller geometric scale?

Googling "2.5 Hz " turns up lots of things relating to brain-waves, deep-sleep and clock escapements, but very little in the way of anything energy-related, other than gravity waves and a certain low-frequency artifact associated with black holes called QPOs. Lower-frequency QPOs are typically 1 to 10 hertz, and they're common in binary star systems with black holes or at least objects denser than a neutron star - the QPO could be the frequency of a *spacetime warp.*

This part is real, folks: it is decidedly NOT Sci-Fi (but it would make a great sub-plot) ! However, the impossible part (seemingly) would be a coupling mechanism for low frequency cosmic gravity wave to a small earthbound device - unless it too is a function of the Hydrogen 21 cm resonance line.

The low-frequency flickering coming from a dense stellar object could be caused by the fabric of space itself churning around in a wave. This is known as Lense-Thirring precession, which evolves out of Einstein's theory of general relativity. There are three other known objects in our galaxy, seemingly as dense as black holes but smaller, which have earned the "micro-quasar" name. One lies just 1,600 light-years from Earth on the way to the center of the Milky Way in the direction of the constellation Sagittarius.

These are "exotic" but nevertheless potential energy sources -
which probably have a strong 4-spatial component - but if they
could be taped on earth, it would take a very serendipitous
discovery.... probably involving the proton at a coherent frequency.

...perhaps a large vacuum tube, of a "lucky" size and just the right hydrogen fill ;-)

Anyway, it is unclear if a 51 Hz base frequency and a 4.9-5 % duty factor really works out to an "effective" 2.5 Hz frequency, using this
particular signal generator - but if  it does, there does not seem
to be any obvious "non-exotic" significance (other than pink noise from the 50 Hz mains)...? Will you settle for exotic?

Didn't think so. Electronic "noise", in general, is related indirectly to 2.5 Hz - i.e. random fluctuations in voltage (or current) the "hiss" we
hear between  stations on an FM tuner,  the "snow" we see when we
tune a TV to an unused channel.  The "whiteness" or the "pinkness"
of noise describes how the energy is distributed in frequency.
White noise is noise whose distribution is constant per cycle of
bandwidth. Pink noise is noise whose energy distribution is constant per
percentage bandwidth. In other words, a 5% band at 50 Hz
(which is 2.5 Hz wide) will have the same amount of energy as a 5%
bandwidth at other frequency. That is not really saying much as to why 2.5 Hz could be important here other than being pink noise from the local mains (unlikely). I like the exotic gravity wave, very "remote" possibility... or better yet - just straight-forward direct coupling to the CMB (cosmic microwave background).

If anyone happens to be lucky enough to the right stuff laying around(i.e. a tube of 21 cm length by 5.24 cm dia) - I'm sure that Fred could give you the correct fill pressure for the parameters ;-)... the problem being that it probably must be actively cooled and heated at the same time to reach an internal coherency level!

One thing is apparent from looking at the testing... JLN has played around with these frequency and duty factor details quite a lot in fine-tuning, presumably trying to get the highest efficiency. And this 2.5 Hz
could be the result, for whatever reason.

Jones

BTW if there is a coupling mechanism between some exotic gravity
wave and hydrogen gas at ~80 torr, is there any place where one
might expect to see large scale evidence of such an effect - in terms of
energy being "coupled" but in a place where it shouldn't be?

Well, there is the aurora borealis but not much hydrogen in it - however both Jupiter and Saturn have a blue corona "aureole" around them.... and it is mostly hydrogen, and with no obvious power source for the blue light emission other than our sun, which seems too far away. Our sun's corona anomaly is a harder to speculate on - as it could be powered by radiation from the stellar core plus something else, such as by hydrinos as Mills says, and who know that there could be other energy components as well.

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